Shift It!

题意翻译

有一个$6×6$的正方形盒子，包含36个木片。每个木片上都有一个字符（A-Z或0-9），且没有重复。 每次操作，你可以将1列整体向上、下移动，或将1行整体向左、右移动。其中，最后一个木片移到原先第一个木片的位置。 写一个程序，找出一个操作序列，使最后矩阵如下： ``` 0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ``` 操作序列不必是最短的，但不能超过100001000010000步。

题目描述

There is a square box $ 6×6 $ in size. It contains $ 36 $ chips $ 1×1 $ in size. Those chips contain 36 different characters — "0"-"9" and "A"-"Z". There is exactly one chip with each character. You are allowed to make the following operations: you may choose one of $ 6 $ rows or one of $ 6 $ columns and cyclically shift the chips there to one position to the left or to the right (for the row) or upwards or downwards (for the column). Those operations are allowed to perform several times. To solve the puzzle is to shift the chips using the above described operations so that they were written in the increasing order (exactly equal to the right picture). An example of solving the puzzle is shown on a picture below. Write a program that finds the sequence of operations that solves the puzzle. That sequence should not necessarily be shortest, but you should not exceed the limit of $ 10000 $ operations. It is guaranteed that the solution always exists.

输入输出格式

输入格式

The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" exactly once.

输出格式

On the first line print number $ n $ , which is the number of operations. On the next $ n $ lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are "L", "R" (to the left, to the right correspondingly, we shift a row), "U", "D" (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from "1" to "6". The rows are numbered from the top to the bottom, the columns are numbered from the left to the right. The number of operations should not exceed $ 10^{4} $ . If there are several solutions, print any of them.

输入输出样例

输入样例 #1

01W345
729AB6
CD8FGH
IJELMN
OPKRST
UVQXYZ

输出样例 #1

2
R2
U3